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What does the k-fold eigenvalue mean in mathematics?
A k-order matrix has k eigenvalues. If there are n identical k eigenvalues, then this eigenvalue is called n-fold eigenvalue.

Eigenvalue is an important concept in linear algebra. It is widely used in mathematics, physics, chemistry, computer and other fields. Let A be an N-order square matrix. If there are several M-nonzero N-dimensional column vectors? X, so Ax=mx holds, then m is said to be an eigenvalue of a.

The non-zero N-dimensional column vector X is called the eigenvector or eigenvector of matrix A, which belongs to (corresponds to) the eigenvalue M, and is called the eigenvector or eigenvector of A for short.

Extended data

The method for finding all eigenvalues and eigenvectors of a matrix is as follows:

Step 1: calculate the characteristic polynomial of;

Step 2: find all the roots of the characteristic equation, that is, all the eigenvalues of;

Step 3: For each eigenvalue of, find the homogeneous linear equations.

Under the action of a transformation, the vector ξ only becomes λ times in scale. ξ is a eigenvector of A, λ is the corresponding eigenvalue (eigenvalue), which is a measurable quantity (in the experiment). Correspondingly, in the theory of quantum mechanics, many quantities cannot be measured. Of course, this phenomenon also exists in other theoretical fields.